mlsanityData to 7 Oct 2026

Is Heterophily A Real Nightmare For Graph Neural Networks To Do Node Classification?

arXiv 2109.05641 ↗First posted 12 Sep 2021cs.LG cs.SIcited by 82

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Abstract (arXiv)

Graph Neural Networks (GNNs) extend basic Neural Networks (NNs) by using the graph structures based on the relational inductive bias (homophily assumption). Though GNNs are believed to outperform NNs in real-world tasks, performance advantages of GNNs over graph-agnostic NNs seem not generally satisfactory. Heterophily has been considered as a main cause and numerous works have been put forward to address it. In this paper, we first show that not all cases of heterophily are harmful for GNNs with aggregation operation. Then, we propose new metrics based on a similarity matrix which considers the influence of both graph structure and input features on GNNs. The metrics demonstrate advantages over the commonly used homophily metrics by tests on synthetic graphs. From the metrics and the observations, we find some cases of harmful heterophily can be addressed by diversification operation. With this fact and knowledge of filterbanks, we propose the Adaptive Channel Mixing (ACM) framework to adaptively exploit aggregation, diversification and identity channels in each GNN layer to address harmful heterophily. We validate the ACM-augmented baselines with 10 real-world node classification tasks. They consistently achieve significant performance gain and exceed the state-of-the-art GNNs on most of the tasks without incurring significant computational burden.

Key facts. Cited by 82 papers in the map (data through 7 Oct 2026). Builds on 28 of its 45 references that are in the map. First posted on arXiv 12 Sep 2021.

Builds on

28 of 45 references.

References · 28

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16 more
  1. 2018Representation Learning on Graphs with Jumping Knowledge Networkscited by 875
  2. 2020Simple and Deep Graph Convolutional Networkscited by 857
  3. 2020Geom-GCN: Geometric Graph Convolutional Networkscited by 821
  4. 2013Speech Recognition with Deep Recurrent Neural Networkscited by 666
  5. 2020Adaptive Universal Generalized PageRank Graph Neural Networkcited by 592
  6. 2019MixHop: Higher-Order Graph Convolutional Architectures via Sparsified Neighborhood Mixingcited by 442
  7. 2021Beyond Low-frequency Information in Graph Convolutional Networkscited by 361
  8. 2019Revisiting Graph Neural Networks: All We Have is Low-Pass Filterscited by 260
  9. 2020Graph Neural Networks with Heterophilycited by 202
  10. 2021Two Sides of the Same Coin: Heterophily and Oversmoothing in Graph Convolutional Neural Networkscited by 182
  11. 2020Non-Local Graph Neural Networkscited by 91
  12. 2021New Benchmarks for Learning on Non-Homophilous Graphscited by 81
  13. 2019Break the Ceiling: Stronger Multi-scale Deep Graph Convolutional Networkscited by 62
  14. 2020Scattering GCN: Overcoming Oversmoothness in Graph Convolutional Networkscited by 57
  15. 2018Geometric Scattering for Graph Data Analysiscited by 49
  16. 2021Simple Truncated SVD based Model for Node Classification on Heterophilic Graphscited by 4

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 1; 2022: 24; 2023: 17; 2024: 21; 2025: 14; 2026: 5.

82 papers.

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  1. 2022Neural Sheaf Diffusion: A Topological Perspective on Heterophily and Oversmoothing in GNNscited by 208
  2. 2022Finding Global Homophily in Graph Neural Networks When Meeting Heterophilycited by 179
  3. 2022Graph Neural Networks for Graphs with Heterophily: A Surveycited by 175
  4. 2024Position: Graph Foundation Models are Already Herecited by 84
  5. 2023Ordered GNN: Ordering Message Passing to Deal with Heterophily and Over-smoothingcited by 67
  6. 2022Characterizing Graph Datasets for Node Classification: Homophily-Heterophily Dichotomy and Beyondcited by 60
  7. 2022Understanding convolution on graphs via energiescited by 58
  8. 2022Gradient Gating for Deep Multi-Rate Learning on Graphscited by 49
  9. 2023MUDiff: Unified Diffusion for Complete Molecule Generationcited by 41
  10. 2022Spectral Augmentation for Self-Supervised Learning on Graphscited by 38
  11. 2024VCR-Graphormer: A Mini-batch Graph Transformer via Virtual Connectionscited by 34
  12. 2022ACMP: Allen-Cahn Message Passing with Attractive and Repulsive Forces for Graph Neural Networkscited by 31
38 more
  1. 2023Beyond Homophily: Reconstructing Structure for Graph-agnostic Clusteringcited by 29
  2. 2024The Heterophilic Graph Learning Handbook: Benchmarks, Models, Theoretical Analysis, Applications and Challengescited by 29
  3. 2023PC-Conv: Unifying Homophily and Heterophily with Two-fold Filteringcited by 28
  4. 2022Effects of Graph Convolutions in Multi-layer Networkscited by 24
  5. 2022High-Order Pooling for Graph Neural Networks with Tensor Decompositioncited by 24
  6. 2023Auto-HeG: Automated Graph Neural Network on Heterophilic Graphscited by 23
  7. 2024Partitioning Message Passing for Graph Fraud Detectioncited by 21
  8. 2022Complete the Missing Half: Augmenting Aggregation Filtering with Diversification for Graph Convolutional Neural Networkscited by 19
  9. 2025Oversmoothing, Oversquashing, Heterophily, Long-Range, and more: Demystifying Common Beliefs in Graph Machine Learningcited by 18
  10. 2021Label-Wise Graph Convolutional Network for Heterophilic Graphscited by 17
  11. 2022Simplified Graph Convolution with Heterophilycited by 17
  12. 2022Node-oriented Spectral Filtering for Graph Neural Networkscited by 17
  13. 2022Single-Pass Contrastive Learning Can Work for Both Homophilic and Heterophilic Graphcited by 14
  14. 2022Homophily modulates double descent generalization in graph convolution networkscited by 13
  15. 2023On Performance Discrepancies Across Local Homophily Levels in Graph Neural Networkscited by 13
  16. 2023MUSE: Multi-View Contrastive Learning for Heterophilic Graphscited by 13
  17. 2024ReactZyme: A Benchmark for Enzyme-Reaction Predictioncited by 13
  18. 2023SIGMA: An Efficient Heterophilous Graph Neural Network with Fast Global Aggregationcited by 10
  19. 2024Similarity-based Neighbor Selection for Graph LLMscited by 10
  20. 2022Restructuring Graph for Higher Homophily via Adaptive Spectral Clusteringcited by 9
  21. 2023Finding Heterophilic Neighbors via Confidence-based Subgraph Matching for Semi-supervised Node Classificationcited by 7
  22. 2023When Do Graph Neural Networks Help with Node Classification? Investigating the Impact of Homophily Principle on Node Distinguishabilitycited by 7
  23. 2023Spatial Heterophily Aware Graph Neural Networkscited by 7
  24. 2024GC4NC: A Benchmark Framework for Graph Condensation on Node Classification with New Insightscited by 7
  25. 2022Revisiting the role of heterophily in graph representation learning: An edge classification perspectivecited by 6
  26. 2022Graph Neural Networks Intersect Probabilistic Graphical Models: A Surveycited by 6
  27. 2024Leveraging Invariant Principle for Heterophilic Graph Structure Distribution Shiftscited by 6
  28. 2024THeGCN: Temporal Heterophilic Graph Convolutional Networkcited by 6
  29. 2022Clenshaw Graph Neural Networkscited by 5
  30. 2024Effective Protein-Protein Interaction Exploration with PPIretrievalcited by 5
  31. 2024Provable Filter for Real-world Graph Clusteringcited by 5
  32. 2025Beyond Fixed Depth: Adaptive Graph Neural Networks for Node Classification Under Varying Homophilycited by 5
  33. 2022From Node Interaction to Hop Interaction: New Effective and Scalable Graph Learning Paradigmcited by 4
  34. 2024Simplified PCNet with Robustnesscited by 3
  35. 2024Learn from Heterophily: Heterophilous Information-enhanced Graph Neural Networkcited by 3
  36. 2024Revealing the Pitfalls and Re-Evaluating the Advancement of Heterophilic Graph Learningcited by 3
  37. 2024Flexible Diffusion Scopes with Parameterized Laplacian for Heterophilic Graph Learningcited by 3
  38. 2024IGNN-Solver: A Graph Neural Solver for Implicit Graph Neural Networkscited by 3

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